Multi-dimensional Fourier transform NMR spectroscopy, and imaging techniques, sometimes referred to as FT-NMR, is an important tool for characterizing the structure of complex molecules and is routinely used to provide information about chemical and biological systems and is becoming progressively important as a diagnostic imaging tool. Artifacts can complicate or lead to false interpretation of the data as well as obscure important spectral or image information. If artifacts result in misinterpretation of the spectral or image data, it should be evident that the resulting confusion will inhibit effective research and progress in our understanding of these systems. For example, the standard spectroscopic method for collection of COSY spectra, will generally produce artifacts at the frequencies of strong narrow resonances which can be confused with peaks that indicate J-coupling.
Methods of eliminating artifacts in 2D-NMR spectra and other NMR data have been previously proposed and include reduction of artifacts arising from such sources as instrument hardware including instabilities in RF phase and flip angle, variations in sampling intervals, lock and magnetic field instability, modulation of NMR signals by sample spinning, instabilities in receiver gain, in RF phase shifting, limited computer word length and others. (See, for example Mehlkcopf, et al. J. Magn. Resonance, 58, 315 (1984), Wider et al. J. Magn. Resonance, 56, 207 (1984) and Nagayama et al. J. Magn. Resonance, 31, 133 (1978)).
Careful instrument design and proper instrument maintenance have been used to remove most of the above stated problems. However, other sources of artifacts have also been identified. These problems include artifacts arising from post data acquisition processing including inaccuracies in Fourier transforms, improper weighing functions, and round-off errors in the Fourier transform.
Techniques have been described to resolve a number of these deficiencies in FT-NMR and other NMR experiments. Specifically, there have been techniques used to remove artifacts which arise from intense narrow resonances. Kramer et al. has disclosed (in U.S. Pat. No. 4,616,182) that certain resonant signal artifacts can be removed by applying a specific type of two-pulse sequence in an imaging system which results in phase variance of artifact signals. This two-pulse sequence causes the artifact signals to be reduced in amplitude or translated from the center of the NMR image acquired.
Glover et al. (in U.S. Pat. No. 4,616,183) has disclosed a method for reducing baseline error components in NMR studies by deriving a baseline error signal and thereafter using this signal to compensate for the error in the acquired NMR data. This invention also discloses certain types of pulse sequences and collection methods for refining signals. In spectroscopy experiments, baseline error corrections have been used to remove t.sub.1 ridges or other artifacts, but require longer acquisition times and do not address discrete artifacts but only baseline offset errors.
Although numerous techniques have been employed to attempt to remove or eliminate artifacts, artifacts in highly symmetrical strong resonances still remain and still plague NMR spectral interpretation or imaging, especially by people that are not extremely well trained in these areas. Artifacts which result from the inherent response of the nuclear spins to the pulse sequences used in the experiments have not been accounted for. The duration of the pulses used in standard types of spectral data collection techniques such as COSY, NOESY or ROSEY arise from the fact that the sample is not allowed to relax completely after the pulse sequence. Therefore, parts of the spectrum that were not allowed to relax will continue throughout the remainder of the sequence, and appear as additional artifacts.
For example, the standard method for collection of COSY 2D-FT-NMR data involves collection of all transients in a single evolution time before incrementing t.sub.1. Appropriate phase cycling to systematically eliminate some artifacts, and cancellation of DC offsets which might arise from imbalanced receiver channels facilitates the method. A pulse sequence conventionally used in this method is shown below: ##EQU1## where x is 0.degree., 90.degree., 180.degree. or 270.degree., y is x+90.degree., ss is the number of dummy steady state pulse cycles which are discarded before transient acquisition, NT is the number of transients averaged, n is the number of t.sub.1 increments, and AT is the acquisition time. The dummy scans are used to establish what in principle should be a steady state, and are not stored or used to obtain NMR data. Ideally, the repetition time for each cycle should be 5-10 times the T.sub.1 value of the proton in the molecule. Using a pulse sequence having a long relaxation delay to compensate for slower relaxing molecules is practically impossible since this would require 12-24 hours to collect a single spectrum. Therefore, zero to one second relaxation delays are normally used to permit reasonably short experiment times (1-2 hours).
When magnetization is not permitted to fully decay (as is typically the case) this method produces systematic t.sub.1 artifacts such as the characteristic "false" COSY cross-peaks that appear at the frequencies of strong narrow resonances.
With short repetition times, longitudinal and transverse magnetization which survives a first 90-t.sub.1 -90 cycle gets carried through additional cycles and contributes to the observed signal in subsequent transients. For example, magnetization from methyl or isolated aromatic protons, which have long relaxation times and produce intense sharp signals, are especially prone to produce artifacts. In fact, these and other protons can produce magnetization components which are carried through many cycles and can contribute to numerous COSY artifacts.
In typical 2D-FT-NMR acquisition methods, phase cycling methods are commonly used which prevent a true steady state magnetization from being established. Calculations of the observed COSY signal after one or more cycles show that residual magnetizations do indeed survive and carry a history of their behavior through successive evolution periods. These residual magnetizations that survive for n cycles will produce artifacts at n times the precession frequencies of the contributing signals.
For example, it can be shown that when using phase cycling techniques, the observable COSY signal at t.sub.2 =0 from an AB system after the first transient (x=0.degree.) is described by: ##EQU2## where .OMEGA..sub.A,B are the precession frequencies of A and B respectively.
It has been found that after a 90.degree. phase shift (x=90.degree.), the observable COSY signal becomes as follows: ##EQU3##
The first four terms of this expression represent the normal COSY diagonal and cross peaks while the last terms show residual magnetization components. These residual magnetization components which survive through a second cycle will carry a history of their behavior through two t.sub.1 evolution periods and show additional cross peaks at 2.OMEGA. in the f.sub.1 dimension. The residual magnetization components in the observable COSY signal could be destroyed by the application of a "homospoil" pulse sequence or a 90.degree. RF pulse sandwiched by two gradient pulses. Unfortunately, application of a "homospoil" pulse would disrupt a stable lock condition in the system and produce a different set of artifacts.
It has thus been found that phase cycling techniques may be used to eliminate undesirable magnetization effects which are not accounted for in standard acquisition techniques but other discrete artifacts are produced. The elimination of the discrete artifacts due to residual magnetization would require the elimination of phase cycling techniques in standard acquisition methods, which are used in the elimination of other artifacts. These contrary requirements have led to a choice being made between which artifact producing components will be accounted for in the acquisition method.
Another problematic aspect of presently known acquisition methods lies in the inability to conduct the NMR experiments in an efficient manner. A typical 2D-FT-NMR spectroscopy experiment will include signal averaging techniques as well as the use of dummy scans or steady state cycles to facilitate the elimination of artifacts. Such an experiment may take as long as several to tens of hours depending on the extent of the data set collected. As the length of the experiment increases, the necessity for backing up the data onto disk also increases to avoid loss of data in the event of power failure or the like. These input/output procedures add to the overall experiment time significantly, thereby exacerbating the problem of inefficient use of a computer for significant periods for only one experiment. These problems become more significant with the advent of 3D-FT-NMR or higher multi-dimensional NMR experiments which require the acquisition of enormous data sets. For example, in a recent publication of a 3D NMR experiment, by Boelens, et al. J. Am. Chem. Soc. 111, 8525 (1989), a spectrum was recorded with two dummy scans and eight scans and resulted in a real 200* 224* 512 data matrix in the t.sub.1, t.sub.2 and t.sub.3 dimension, respectively. The experiment took approximately 137 hours of machine time, with disk input/output operations accounting for about 29 hours of this total. Similarly, the acquisition methods used in imagining techniques may lead to visual artifacts which obscure important diagnostic information. The present methods of reducing artifacts in imaging require additional steady state cycles or pulse sequences to establish steady state magnetization, measure error components or attempt to remove residual magnetization effects. All these methods will add to some degree the acquisition time needed to obtain as error-free data as possible which may be unacceptable in imaging due to patient comfort and similar considerations.